Cryptanalysis of Some Protocols Using Matrices over Group Rings

  • Mohammad EftekhariEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10239)


We address a cryptanalysis of two protocols based on the supposed difficulty of discrete logarithm problem on (semi) groups of matrices over a group ring. We can find the secret key and break entirely the protocols.


Key exchange Symmetric groups Representation of algebras 


  1. 1.
    Banin, M., Tsaban, B.: A reduction of semigroup DLP to classic DLP. Des. Codes Crypt. 81, 75–82 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Childs, A., Ivanyos, G.: Quantum computation of discrete logarithms in semigroups. J. Math. Cryptology 8(4), 405–416 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    James, G.D.: The Representation Theory of the Symmetric Groups, vol. 682. Springer, Heidelberg (1978). SLNzbMATHGoogle Scholar
  4. 4.
    Kahrobaei, D., Koupparis, C., Shpilrain, W.: Public key exchange using matrices over group rings. G.C.C. 5(1), 97–115 (2013)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Kahrobaei, D., Koupparis, C., Shpilrain, W.: A CCA secure cryptosystem using matrices over group rings. Amer. Math. Soc. Contemp. Math. 633, 73–80 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Menezes, A.J., Wu, Y.-H.: The discrete logarithm problem in \(GL_n({\mathbb{F}}_q)\). ARS Combinatorica 47, 23–32 (1997)Google Scholar
  7. 7.
    Myasnikov, A., Ushakov, A.: Quantum algorithm for discrete logarithm problem for matrices over finite group rings.Google Scholar
  8. 8.
    Odonne, R., Varadharajan, D., Sanders, P.: Public key distribution in matrix rings. Electron. Lett. 20, 386–387 (1984)CrossRefGoogle Scholar
  9. 9.
    Serre, J.P.: Représentations linéaires des groupes finis. Hermann, Paris (1967)zbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.LAMFA, CNRS UMR 7352, Université de Picardie – Jules VerneAmiensFrance

Personalised recommendations